Octal ToolsFree Interactive Tool

Octal Arithmetic Calculator

Perform addition, subtraction, multiplication, and division directly on base-8 octal numbers. Designed for software developers, electrical engineers, students, and computer architecture researchers requiring deterministic client-side accuracy.

Engine: Client-Side Verified (0ms Latency)

Operation

First Octal Number (A)

Enter base-8 digits (0 through 7 only).

Second Octal Number (B)

Calculated Output

Primary Representation

Calculating...

Step-by-Step Mathematical Proof

Active Derivation

Ready. Enter input above to generate derivation.

Concept

What Is Octal Arithmetic Calculator?

The Octal Arithmetic Calculator performs basic arithmetic operations (addition, subtraction, multiplication, and division) directly in base 8 without converting to base 10 first. Base 8 uses eight digits (0 through 7) and wraps columns at 8 rather than 10.

Methodology

How Does It Work?

During addition, any column sum of 8 or more produces an octal carry (sum - 8 with carry 1). During subtraction, borrowing from a neighboring higher column adds 8 to the current column. During multiplication and division, base-8 place values (1, 8, 64, 512) govern column products and remainders.

Formula & Rules

Mathematical Algorithm

A_8 \odot B_8 = R_8 \quad (\odot \in \{+, -, \times, \div\}) \quad \text{where base } = 8

Worked Problem

Step-by-Step Example

Add 75_8 + 23_8: Column 0: 5 + 3 = 8 -> 8 mod 8 = 0, carry 1 Column 1: 7 + 2 + 1 (carry) = 10 -> 10 mod 8 = 2, carry 1 Column 2: 1 (carry) Result: 120_8 (which equals decimal 80).